KNIGHT COVERING 31x32

Although this website has featured only square chessboards until now, the 31x32 board is a case of special interest. Monier's pattern, discovered by J. M. Monier of Marseilles in the 1970's, is an exceptionally efficient placement of knights in which each knight covers 8 squares of the board. Until Sept. 2003, when a second pattern was discovered by Frank Rubin, it was believed that this was the only pattern that could achieve such a high coverage.

It has long been assumed that for large chessboards the most efficient covering would have to use Monier's pattern. The first such efficient covering was found by Bernard F. Lemaire, and uses 152 knights. Unfortunately, this is not optimal, as the 148-knight covering below demonstrates. Beneath that is a 151-knight covering using Monier's pattern.

A 148-knight covering of a 31x32 board
Found Oct. 3, 2003 by Frank Rubin

A 151-knight covering of a 31x32 board using Monier's pattern.
The pattern is shown with the black knights.
Found Oct. 10, 2003 by Frank Rubin

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